My husband financed his undergraduate by credit card – running up balances and paying them off by working multiple summer jobs. Not exactly the most economical solution in terms of interest rates, etc, but his only option st the time.
Monthly payment plans through the school could be an option that doesn’t require a cosigner as well.
For those questioning the car: it’s often necessary to get to work.
But those questioning Cedarville are right: a private school that does not meet full need should be off the table. Look at your in-state and regional compact schools for lower price tags.